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service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the elf-service island at a particular time, and let y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. p(x,y) 0 y 1 2 0 0.10 0.05 0.01 1 0.06 0.20 0.07 2 0.05 0.14 0.32 a) What is P(X: = 1 and Y = 1)? P(X= 1 and Y = 1) = [ b) Compute P(X<1 and Y≤ 1). P(X ≤ 1 and Y≤ 1): c) Give a word description of the event {X+0 and Y #0}. O At least one hose is in use at both islands. O At most one hose is in use at both islands. O One hose is in use on both islands. O One hose is in use on one island. Compute the probability of this event. P(X+0 and Y = 0) =

service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the elf-service island at a particular time, and let y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. p(x,y) 0 y 1 2 0 0.10 0.05 0.01 1 0.06 0.20 0.07 2 0.05 0.14 0.32 a) What is P(X: = 1 and Y = 1)? P(X= 1 and Y = 1) = [ b) Compute P(X<1 and Y≤ 1). P(X ≤ 1 and Y≤ 1): c) Give a word description of the event {X+0 and Y #0}. O At least one hose is in use at both islands. O At most one hose is in use at both islands. O One hose is in use on both islands. O One hose is in use on one island. Compute the probability of this event. P(X+0 and Y = 0) =

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. p(x, y) 0 1 2 0 y 1 0.10 0.05 0.01 0.06 0.20 0.07 0.05 0.14 0.32 (a) What is P(X= = 1 and Y = 1)? P(X= 1 and Y= 1) = [ P(X ≤ 1 and Y ≤ 1) =| (b) Compute P(X ≤ 1 and Y≤ 1). 2 (c) Give a word description of the event { X0 and Y#0}. O At least one hose is in use at both islands. At most one hose is in use at both islands. O One hose is in use on both islands. O One hose is in use on one island. Compute the probability of this event. P(X+0 and Y 0) =|
Transcribed Image Text:A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. p(x, y) 0 1 2 0 y 1 0.10 0.05 0.01 0.06 0.20 0.07 0.05 0.14 0.32 (a) What is P(X= = 1 and Y = 1)? P(X= 1 and Y= 1) = [ P(X ≤ 1 and Y ≤ 1) =| (b) Compute P(X ≤ 1 and Y≤ 1). 2 (c) Give a word description of the event { X0 and Y#0}. O At least one hose is in use at both islands. At most one hose is in use at both islands. O One hose is in use on both islands. O One hose is in use on one island. Compute the probability of this event. P(X+0 and Y 0) =|
(d) Compute the marginal pmf of X. 0 Px(x) Compute the marginal pmf of Y. y Py(y) 0 1 1 Using Px(x), what is P(X < 1)? P(X ≤1)=[ 2 2 (e) Are X and Y independent rv's? Explain. OX and Y are not independent because P(z,y) #Px(z) · Py(y). OX and Y are independent because P(x, y) = Px (1) - Py (y). OX and Y are not independent because P(x, y) = Px(z) - Py(y). OX and Y are independent because P(x, y) #Px (2) - Py (Y).
Transcribed Image Text:(d) Compute the marginal pmf of X. 0 Px(x) Compute the marginal pmf of Y. y Py(y) 0 1 1 Using Px(x), what is P(X < 1)? P(X ≤1)=[ 2 2 (e) Are X and Y independent rv's? Explain. OX and Y are not independent because P(z,y) #Px(z) · Py(y). OX and Y are independent because P(x, y) = Px (1) - Py (y). OX and Y are not independent because P(x, y) = Px(z) - Py(y). OX and Y are independent because P(x, y) #Px (2) - Py (Y).
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